The average score on the Mathematics part of the SAT exam for males is 534 with a standard deviation of 118, while the average score for females is 500 with a standard deviation of 112.
(a) If random samples are taken with 40 males and 60 females, find the mean and standard deviation of the distribution of differences in sample means, x̅_m − x̅_f , where x̅_m represents the sample mean for the males and x̅_f represents the sample mean for the females.

(b) Repeat part (a) if the random samples contain 400 males and 600 females.

(c) What effect do the different sample sizes have on center and spread of the distribution?

involve scores from the high school graduating class of 2010 on the SAT(Scholastic Aptitude Test).